12.4.2 Pattern Correlation Methods

12.4.2.1 Horizontal patterns

Results from studies using pattern correlations were reported extensively in
the SAR (for example, Santer et al., 1995, 1996c; Mitchell et al., 1995b). They
found that the patterns of simulated surface temperature change due to the main
anthropogenic factors in recent decades are significantly closer to those observed
than expected by chance. Pattern correlations have been used because they are
simple and are insensitive to errors in the amplitude of the spatial pattern
of response and, if centred, to the global mean response. They are also less
sensitive than regression-based optimal detection techniques to sampling error
in the model-simulated response. The aim of pattern-correlation studies is to
use the differences in the large-scale patterns of response, or "fingerprints",
to distinguish between different causes of climate change.

Strengths and weaknesses of correlation methods
Pattern correlation statistics come in two types - centred and uncentred
(see Appendix 12.3). The centred (uncentred) statistic
measures the similarity of two patterns after (without) removal of the global
mean. Legates and Davis (1997) criticised the use of centred correlation in
detection studies. They argued that correlations could increase while observed
and simulated global means diverge. This was precisely the reason centred correlations
were introduced (e.g., Santer et al., 1993): to provide an indicator that was
statistically independent of global mean temperature changes. If both global
mean changes and centred pattern correlations point towards the same explanation
of observed temperature changes, it provides more compelling evidence than either
of these indicators in isolation. An explicit analysis of the role of the global
mean in correlation-based studies can be provided by the use of both centred
and uncentred statistics. Pattern correlation-based detection studies account
for spatial auto-correlation implicitly by comparing the observed pattern correlation
with values that are realised in long control simulations (see Wigley et al.,
2000). These studies do not consider the amplitude of anthropogenic signals,
and thus centred correlations alone are not sufficient for the attribution of
climate change.

Wigley et al. (1998b) studied the performance of correlation statistics in
an idealised study in which known spatial signal patterns were combined with
realistic levels of internal variability. The statistics were found to perform
well even when the signal is contaminated with noise. They found, in agreement
with Johns et al. (2001), that using an earlier base period can enhance detectability,
but that much of this advantage is lost when the reduced data coverage of earlier
base periods is taken into account. They also found that reasonable combinations
of greenhouse gas and aerosol patterns are more easily detected than the greenhouse
gas pattern on its own. This last result indicates the importance of reducing
the uncertainty in the estimate of aerosol forcing, particularly the indirect
effects. In summary, we have a better understanding of the behaviour of pattern
correlation statistics and reasons for the discrepancies between different studies.